Related papers: Exact Sampling from Determinantal Point Processes
Direct Preference Optimization (DPO) has emerged as a stable, scalable, and efficient solution for language model alignment. Despite its empirical success, the optimization properties, particularly the impact of samplers on its convergence…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
Predicting when and where events will occur in cities, like taxi pick-ups, crimes, and vehicle collisions, is a challenging and important problem with many applications in fields such as urban planning, transportation optimization and…
We consider the task of MCMC sampling from a distribution defined on a discrete space. Building on recent insights provided in [Zan19], we devise a class of efficient continuous-time, non-reversible algorithms which make active use of the…
Molecular Dynamics (MD) simulations are fundamental computational tools for the study of proteins and their free energy landscapes. However, sampling protein conformational changes through MD simulations is challenging due to the relatively…
Sampling is a key operation in point-cloud task and acts to increase computational efficiency and tractability by discarding redundant points. Universal sampling algorithms (e.g., Farthest Point Sampling) work without modification across…
Most exact algorithms for general partially observable Markov decision processes (POMDPs) use a form of dynamic programming in which a piecewise-linear and convex representation of one value function is transformed into another. We examine…
Sampling techniques are used in many fields, including design of experiments, image processing, and graphics. The techniques in each field are designed to meet the constraints specific to that field such as uniform coverage of the range of…
Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…
Large dimensional least-squares and regularised least-squares problems are expensive to solve. There exist many approximate techniques, some deterministic (like conjugate gradient), some stochastic (like stochastic gradient descent). Among…
We consider determinantal point processes on the $d$-dimensional unit sphere $\mathbb S^d$. These are finite point processes exhibiting repulsiveness and with moment properties determined by a certain determinant whose entries are specified…
Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…
In this paper we aim to construct infinite dimensional versions of well established Piecewise Deterministic Monte Carlo methods, such as the Bouncy Particle Sampler, the Zig-Zag Sampler and the Boomerang Sampler. In order to do so we…
We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random…
The maximum a posteriori (MAP) inference for determinantal point processes (DPPs) is crucial for selecting diverse items in many machine learning applications. Although DPP MAP inference is NP-hard, the greedy algorithm often finds…
Direct Preference Optimization (DPO) has emerged as a de-facto approach for aligning language models with human preferences. Recent work has shown DPO's effectiveness relies on training data quality. In particular, clear quality differences…
Decision Trees are prominent prediction models for interpretable Machine Learning. They have been thoroughly researched, mostly in the batch setting with a fixed labelled dataset, leading to popular algorithms such as C4.5, ID3 and CART.…
Markov Chain Monte Carlo (MCMC) algorithms are routinely used to draw samples from distributions with intractable normalization constants. However, standard MCMC algorithms do not apply to doubly-intractable distributions in which there are…
We introduce Divnet, a flexible technique for learning networks with diverse neurons. Divnet models neuronal diversity by placing a Determinantal Point Process (DPP) over neurons in a given layer. It uses this DPP to select a subset of…